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302. Creatures

302.1. A player who has priority may cast a creature card from his or her hand during a main phase of his or her turn when the stack is empty. Casting a creature as a spell uses the stack. (See rule 601, "Casting Spells.")

302.2. When a creature spell resolves, its controller puts it onto the battlefield under his or her control.

Only when the spell resolves is the creature actually on the battlefield. You can counter it, because while on the stack that creature isn't actually a "creature" but a "creature spell".

114.2. Only permanents are legal targets for spells and abilities, unless a spell or ability (a) specifies that it can target an object in another zone or a player, (b) targets an object that can't exist on the battlefield, such as a spell or ability, or (c) targets a zone.

You can only damage a creature when it is already on the battlefield. Because that creature has protection from all colors, you cannot target it or deal damage to it with colored spells.

No, you cannot damage or destroy creatures on the stack, because creatures do not exist on the stack, "Creature Spells" do. When a spell or ability is referring to a creature, and it doesn't use "card," "spell," or "source," it is referring to a creature permanent. Permanents only exist on the battlefield. Damage can only be dealt to creature/planeswalker permanents (or Players, who are not Objects).

109.2. If a spell or ability uses a description of an object that includes a card type or subtype, but doesn’t include the word “card,” “spell,” “source,” or “scheme,” it means a permanent of that card type or subtype on the battlefield.

110.1. A permanent is a card or token on the battlefield. A permanent remains on the battlefield indefinitely. A card or token becomes a permanent as it enters the battlefield and it stops being a permanent as it’s moved to another zone by an effect or rule.

111.1. A spell is a card on the stack.

119.1a Damage can’t be dealt to an object that’s neither a creature nor a planeswalker.

You also cannot destroy a creature through some other means than damage for precisely the same reasons.

701.6a To destroy a permanent, move it from the battlefield to its owner’s graveyard.